Hob for cutting gear teeth



Feb. 27, 1923. 1,446,910 J. M. LABBERTON -HOB FOR CUTTING GEAR TEETH Filed Mar. 15, 1920 1 33.4J.6K.7.@ s 1.

WITNESSES: I INVENTOR ffJfibw/mu Jokn/IZ Labberzon MED STATES 1 1,446,916 EN OFFIC' JOHN MADISON LAIBBERTON, OF WILKINSBURG, PENNSYLVANIA, ASSIGNOR TO WEST- INGHOUSE ELECTRIC & MANUFACTURING COMPANY, A CORPORATION OF PENN- SYLVANIA.

HOB FOR CUTTING GEAR TEETH.

Application filed March 13, 1920. Serial No. 365,382.

I '0 all whom it may concern Be it known that I," JOHN MADISON LAB- BERTON, a citizen of the United States, and a resident of Wilkinsburg, in the county of Allegheny and State of Pennsylvania, have invented a new and useful Improvement in Hobs for Cutting Gear Teeth,-of which the following is a specification.

My invention relates to gear teeth as employed on pinions and gear wheels and particularly to hobs for cutting such teeth, and it has for its object to provide a hob for cutting involute teeth that shall be stronger than those commonly employed at present and that shall mesh with adequate clearance, with a substantially uniform percentage of rolling and with an optimum pressure angle. irrespective of the gear ratio employed.

Heretofore, a constant pressure angle has been used in the design of gear teeth of the involute form over the entire range of gear ratios and of gear wheel diameters and it was possible to use one hob to cut the teeth for a co-operating pinion and gear wheel of any relative number of teeth and of any number of teeth in the tWo wheels so long as the same diametral pitch .was used.

This method has the following disadvantages. In the case of a pinion having a. relatively small number of teeth meshing with a gear wheel having a large number of teeth, the form of the teeth in both wheels must be modified in order to permit the gear and the pinion to operate properly without interference. The amount of rolling between co-operating gear teeth will vary with the gear ratio used, with the result that a gear or a pinion which may operate properly and with relatively small wear in one application will be subjected to much greater Wear in another application. The addendum and the dedendum of the gear teeth have been made substantially equal save for a small amount of clearance at the roots of the teeth,

resulting in the thickness of the teeth of both the pinion and the-gear at the pitch circle being the same and, consequently, of relatively different strengths.

In my copending application Serial No.

336,069, filed Nov. 6, 1919, and assigned to the \Vestinghouse Electric & Manufacturing (0.. I have disclosed a method of designing involute. teeth for co-operating gear wheels based upon a mathematical analysis of the elements entering into the problem of meshmathematical analysis of ing gear teeth. Having once made this analysis and having derived relatively simple formulae, I am able, by their use, to calculate the proper constants to be used in laying out the tooth form. The data usually available when laying out the form of teeth for a set of co-operating gear wheels includes the gear ratio, the gear-center distance and the desired diametral pitch. By the use of the above-mentioned formulae embodying my method, I calculate the pressure angle, the addendum and the dedendum of the teeth and the relative tooth thickness at'the pitch circle, and may then proceed to lay out the tooth form for the particular application. After, the dimensions of the gear teeth have been determined, it is possible to determine the dimensions of the hobs which are required to cut the teeth of the pinion and of the gear wheel, respectively.

The method of designing the gear teeth will be here given, in order to bring out the specific differences between the hobs used in cutting teeth and the hobs used .for cutting the usual form of involute teeth.

Referring to the drawings, Figure 1 is a diagram showing two co--operating teeth of a spur pinion and gear, together with certain other details which will be used in the the problem. Fig. 2 is a curve showing the ratio of the thicknesses of the teeth of the #1 and #2 gear wheels at the pitch circle, as a function of the gear ratio. Fig. 3 is a .view, in side elevation, of 'a hob which may be used in cutting such teeth, and Fig. 4' is an end view of such a hob.

Referring to Figure 1 4 Let r zradius of pitch circle of the #1 gear wheel. 1'. ,:radius of pitch circle of the #2 gear wheel. k zradius of base circle of the #1 gear wheel. v. .:radi us of base circle of the #2 a gear wheel.

g zNo. of teeth of the #1 gear wheel. g zNo. of teeth of the #2 gear wheel.

representing 'code of #2 gear 6 mm, represents the base circle-of the #1.

gear wheel.

yy represents gear wheel.

2 represents the center of the #1 gear wheel.

2 represents the center of the #2 wheel. V

2 .2 represents the line joining the gear centers.

0 represents the point at which the line as, intersects the pitch circles of the two car wheels.

my representsthe line of pressure of the co-operating gear teeth drawn as a tangent to the twobase circles new, and yy F or the purpose'of our analysis, the two curves S and T, representing the co-operating gear teeth surfaces, are assumed to pass through the point 0.

Draw spective gear wheel to the line my.

The angles 02 w and 02 g are equal and designated by the letter a. The in- S will meet its base circle was, at a and the involute T will meet its base circle yy at a point 3 Draw the linese w and 2 3 and by the construction the angle wz w will be equal to y z y and may be designated by I).

Let s, rep-resent a point on the curve S at which the tip of the curve T of the cooperating tooth will first make contact under operating conditions. The evolute of the involute curve 00 5), will be the are 00 00, ind we may designate the angle m z w Let t, represent a point on the curve T at which the tip of the curve of the coperating tooth will last make contact under operating conditions. The are 31 will be the evolute of the involute curve 'y t and we may designate the angle y' z y the base circle of the #2 gear centers at right angles The length The length k b (by calculus).

of the line ocozzr sin 0;.

of the involute 00 0;:

Consider the section 8 0 of the involute gendrawn from base wheel must mate with the section S.

the line 2 a: and e g from the reof the line a gal- :4", cos a.

aeaem erated by the evolute of angle aw w which is equal to (12-0 k b k c k a S 2 2 b -'C I that the #1 gear wheel rotates through (b-0 radians, the tooth contact surface S is always perpendicular to the line of pressure my.

If the #1 gear wheel rotates through (Ia-0 radians, the

#2 gear wheel will cor (b c radians and a portion of the contact surface '11 on the co-operating tooth of the #2 gIeJar et part of T If it is assumed respondingly rotate through 2* 2 this co-operating surface be that between the parts 0 an 23 The angle gag if 1) The angle 1 .2

b +%(b c The length of the co-operating surface t,0 is, from the drawing The proportion of the surface T on which rolling of the two co-operating tooth surfaces occurs is sliding of the two surfaces occurring over the remainder thereof.

Let this ratio F5 be represented by K.

out teeth, i. e., two cylindrical surfaces havthe are {0073 of the ing frictional driving engagement. The designer must therefore decide what amount of rolling is desired or What amount will give the best operating results, and it may be noted that K will be a number less than unity; i

If we represent the ratio 21 '2 by R and substitute in the above formula we get 5+0 '3' 1 If it???) c and in a similar manner We may obtain than the present standard involute tooth.

Thi is also equal to g2 The length of contact tooth from the drawing surface 25 25 of the and as k =r cos a It may be noted that the angle of action for the #1 gear wheel I b c1 b c2 R and for the #2 gear wheel I WWW-6.31m The addendum is .2 t -r Therefore the addendum of #2 gear wheel tooth Similarly, the addendum for the #1 gear wheel tooth Fig. 2 shows a curve representing the relative thicknesses of the teeth of the #1 and #2 gear wheels at the pitch line as a function of the gear ratio B. This curve was determined by using the above formulae to calculate certain dimensions of the gear teeth and then by so proportioning the pitchline thicknesses of the #1 and #2 gear Wheel teeth as to make them of substantially equalcalculated strength.

For the purpose of illustrating the use of the above method and of the formulae, it may be assumed that it is desired to lay out a tooth form for a pair of cooperating spur gear Wheels having a given distance between #2 gear Wheel reference to Fig. of line z t, (not gear centers, the diametrical pitch being known, as is also the desired gear ratio. Select a value of K (percentage of rolling) somewhat lower than unity. Calculate c and 0 by using the formulae (2) and (3). Then substitute these values in formula (4) and solve for a the pressure angle, noting that bztan a from formula (1).

Then determine the addenda for the respective gear Wheels, using formulae and V (6), and allow the usual clearance at the root of the teeth. By reference to the curve of Fig. 2, the relative thicknesses -ofthe teeth of the tWo gear wheels at the pitch circle may be determined.

We now have the pressure angle, the addenda for the teeth of the respective gear wheels, and the tooth thicknesses at the pitch line, and We.

the teeth of the two gear wheels.

may proceed to layout While 1 have illustrated the use of my vary not only with the gear ratio but also method for determining the dimensions of with the number of teeth in the gear wheels. the teeth of spur gear wheels, it may be Referring particularly to Fig. 3, the angle used also for bevel gear wheels and for helibetween the edge of the cutting face and a cal gear teeth. line drawn at right angles to the axis of the By the use of the above method, I provide hob is equal to the pressure angle a of Fig. cc a gear tooth, the pressure angle of which 1. The total depth of the cutting faces varies not only with-the gear ratio but also represented by the dimension d in Fig. 3, is with the number of teeth in the respective the total depth of the tooth which is'cut by gear wheels. By inspection of the formulae, means of said hob. it may be noted that the pressure angle is I desire that only such limitations shall be larger for the higher gear ratios, which will placedupon my invention as are imposed by tend to reduce interference between the cothe prior art or are specifically set forth in operating teeth. The location of the points the appended claims. i of initial and of final contact between co- 1 claim as my invention: operating teeth is a function of the amount 1. A hob for cutting a predetermined 74B of rolling action and of the gear ratio and, number of teeth in one of a pair of co-opas the values of 0 and 0 can never be zero, crating gear wheels, said hob having cut- I (see formulae 2 and 3) these two points will ting faces the angle between the sides 0 always be outside of the addendum circle of Which-is determined in accordance with the the co-operating gear Wheel, and hence, desired amount of rolling action between co- 75 there can be no interference. The addenda operating teeth and which angle is substanof the respective teeth is different, thus retially equal to the pressure angle of the sulting in a stronger tooth than would be teeth to be cut.

obtained with the method heretofore used. 2. The method of designing hobs for out- By proportioning the pitch-line thicknesses ting teeth in two gear wheels of different of the teeth of the #1 and #2 gear wheels pitch diameters which consists in determinin accordance with the curve shown in Fig. ing the amount of rolling action desired be- 2, the teeth in the two gear wheels may be tween co-operating gear teeth, in calculatmacle substantially equal in strength. The ing the pressure angle and the addenda of rolling action is substantially the same for the teeth, in calculating the pitch line thickall gear ratios and for all numbers of teeth ness of the teeth of the respective gear in the respective gear wheels. wheels, and in forming the cutting faces 0 Figs. 3 and t show one form of hob which each hob at an angle substantially equal to may be used to cut gear teeth designed by the pressure angle -of the teeth and of a the use of the above method and it may be depth substantially equal to the depth of the ac noted that one hob will be required to cut teeth of the gearwhich it is designed to the teeth on the pinion and another hob to cut. cut the teeth on the gear wheel. This is for 3. The method of designing hobs for outthe reason that the thickness of the pinion ting teeth in two gear wheels of different tooth at the pitch line is always greater than pitch, which consists in determining the the thickness of the gear wheel tooth at its amount. of rolling action desired between pitch line. To illustrate, it may be menco-operating gear teeth, in calculating the tioned that, in a particular co-operating pressure angle and the addenda of the pinion and gear wheel, the thickness of the teeth, in calculating the pitch line thickness pinion teeth at the pitch line was .45 and of the teeth of the respective gear wheels, the thickness of-the gear wheel teeth atthe and in forming the cutting faces of the hobs pitch line was .3 54". of a depth proportional to the desired It may also be noted that such a pair of amount of rolling action and at an angle hobs is adapted to be used for cutting the substantially equal to the angle of pressure. teeth on one pair of co-operating gear wheels In testimony whereof, l have hereunto 05 only, inasmuch as the dimensions of the subscribed my name this 5th day of March,

teeth and the pressure angle and, conse- 1920. quently, certain dimensions of the hobs will JOHN MADISON LABBERTON. 

